Power Coefficient Of Reactivity Research Articles

Implication of Removal of Cadmium Poison on Neutron Flux and Related Parameters in Nigeria Research Reactor - 1

Nigeria’s Miniature Neutron Source Reactor (MNSR) has been in function since 2004. Over the ten years of operation, several installation and calculation were made on Nigeria research reactor-1 for the safety under project supply agreements and IAEA member state. In this work, we show the implication of removal of cadmium poison on neutron flux and related parameter by using lattice code WIMS and core analysis code CITATION, to automatically carry out each of the following calculations on MNSRs: core excess reactivity, verification of some safety criteria, and calculating various temperature coefficients of reactivity. Results obtained before, after and after removal of cadmium poison are: excess core reactivity (3.72, 2.96 and 2.92) mk, fuel temperature coefficient reactivity (-0.0018, -0.0054 and -0.0060) mk/°C, power coefficient of reactivity (-0.2527, -0.1260 and 0.0575) mk/kW and predicted power of (15.23, 14.65 and 14.99) kW with coolant temperature (12.43, 12.10 and 12.50) °C respectively. The result will not only boost the sample handling capabilities of NIRR-1 but will also provide useful data to the MNSR community for upgrading their reactors and specifically ageing management.

Space independent xenon oscillations control in VVER reactor: A bifurcation analysis approach

A comprehensive parametric bifurcation analysis has been carried out in order to control space independent xenon instabilities in a reduced order model of VVER 1000 reactor. A lumped parameter kinetic model which takes into account the fundamental mode of reactor power is developed to describe nonlinear dynamic behavior of the reactor. The usual state space controller design techniques for such a model often require canonical representations which impose certain challenges in practical implementation of a rather easy and feasible control task. Bifurcation control methods are therefore resorted which rely basically on a physical intuition into the reactor nonlinear behavior. Reactor local stability behavior is essentially related to thermal feedback effects represented by the power coefficient of reactivity, a variant parameter during system operation causing Hopf bifurcation induced oscillations. The plant is shown to experience instability as the bifurcation parameter takes value in the working region of the reactor. Control procedure is thereby carried out accordingly via manipulation of power coefficient of the reactivity as the Hopf parameter. Taking into account the power (temperature) dependent origin of the selected Hopf parameter, a Washout filter is designed and implemented to relocate this parameter outside the instability region through application of reactor power as the state feedback variable. Numerical simulations exhibit quite reasonable performance of the proposed controller to maintain reactor stability.

Evaluation of CANDU6 PCR (power coefficient of reactivity) with a 3-D whole-core Monte Carlo Analysis

The power coefficient of reactivity (PCR) is a very important parameter for inherent safety and stability of nuclear reactors. The combined effect of a relatively less negative fuel temperature coefficient and a positive coolant temperature coefficient make the CANDU6 (CANada Deuterium Uranium) PCR very close to zero. In the original CANDU6 design, the PCR was calculated to be clearly negative. However, the latest physics design tools predict that the PCR is slightly positive for a wide operational range of reactor power. It is upon this contradictory observation that the CANDU6 PCR is re-evaluated in this work. In our previous study, the CANDU6 PCR was evaluated through a standard lattice analysis at mid-burnup and was found to be negative at low power. In this paper, the study was extended to a detailed 3-D CANDU6 whole-core model using the Monte Carlo code Serpent2. The Doppler broadening rejection correction (DBRC) method was implemented in the Serpent2 code in order to take into account thermal motion of the heavy uranium nucleus in the neutron-U scattering reactions. Time-average equilibrium core was considered for the evaluation of the representative PCR of CANDU6. Two thermal hydraulic models were considered in this work: one at design condition and the other at operating condition. Bundle-wise distributions of the coolant properties are modeled and the bundle-wise fuel temperature is also considered in this study. The evaluated nuclear data library ENDF/B-VII.0 was used throughout this Serpent2 evaluation. In these Monte Carlo calculations, a large number of neutron histories were simulated to reduce standard deviation of the k-effective values to ∼1pcm. The evaluated PCRs were compared with the official PCR value of the CANDU6 core calculated by RFSP-IST code. It was found that the CANDU6 PCR can be clearly negative at low power ranges for both design and operating conditions.

Negative power coefficient on PHWRs with CARA fuel

A study of power coefficient of reactivity in heavy water reactors is made analyzing the reactivity components of fuels with several modifications oriented at reducing the coefficient. A cell model is used for neutronics calculations; a non-linear two dimensional model is used to evaluate the thermal changes that follow a power change; and a levelized unit energy cost model is used to assess the economical feasibility of the design changes introduced to reduce power coefficient.The necessity of modelling all the aforementioned quantities in a coupled scheme is stressed, as a strong interdependence was found. A series of design changes complied with a negative power coefficient of reactivity, with a feasible power radial distribution and with low refuelling cost. Some investigation lines that exceed the fuel cell study and deal with the plant operation are marked as potentially addressing the stable operation of big heavy water reactors.

Neutronic analysis of the Geological Survey TRIGA Reactor

The United States Geological Survey TRIGA Reactor (GSTR) is a 1MW reactor located in Lakewood, Colorado. In support of the GSTR’s relicensing efforts, this project developed and validated a Monte Carlo N-Particle Version 5 (MCNP5) model of the GSTR reactor. The model provided estimates of the excess reactivity, power distribution and the fuel temperature, water temperature, void, and power reactivity coefficients for the current and limiting core. The MCNP5 model predicts a limiting core excess reactivity of $6.48 with a peak rod power of 22.2kW. The fuel and void reactivity coefficients for the limiting core are strongly negative, and the core water reactivity coefficient is slightly positive, consistent with other TRIGA analyses. The average fuel temperature reactivity coefficient of the full power limiting core is −0.0135$/K while the average core void coefficient is −0.069$/K from 0% to 20% void. The core water temperature reactivity coefficient is+0.012$/K.

Measurement of the power and temperature reactivity coefficients of the RTP TRIGA reactor

This paper presents the experimental results of the power and temperature coefficients of reactivity of the RTP TRIGA reactor at the Malaysian Nuclear Agency. The power coefficient of reactivity obtained was approximately −0.26¢kW−1 (−1.81×10−5kW–1), and the measured temperature reactivity coefficient of the reactor was −0.82¢°C−1 (−5.77×10−5°C−1) and −1.15¢°C−1 (−8.08×10−5°C−1) in IFE C12 and IFE F16, respectively. The power defect, which is the change in reactivity taking place between zero power and the power of 850kW was ∼2.19$. Because of the negative temperature coefficient, a significant amount of reactivity is needed to compensate for the temperature change and allows the reactor to operate at the higher power levels in steady state. Throughout this experiment, it is the temperature of the fuel that was measured, not the isothermal temperature coefficient (ITC), which comprises both moderator and fuel.

THE IMPACT OF POWER COEFFICIENT OF REACTIVITY ON CANDU 6 REACTORS

The combined effects of reactivity coefficients, along with other core nuclear characteristics, determine reactor core behavior in normal operation and accident conditions. The Power Coefficient of Reactivity (PCR) is an aggregate indicator representing the change in reactor core reactivity per unit change in reactor power. It is an integral quantity which captures the contributions of the fuel temperature, coolant void, and coolant temperature reactivity feedbacks. All nuclear reactor designs provide a balance between their inherent nuclear characteristics and the engineered reactivity control features, to ensure that changes in reactivity under all operating conditions are maintained within a safe range. The CANDU ® reactor design takes advantage of its inherent nuclear characteristics, namely a small magnitude of reactivity coefficients, minimal excess reactivity, and very long prompt neutron lifetime, to mitigate the demand on the engineered systems for controlling reactivity and responding to accidents. In particular, CANDU reactors have always taken advantage of the small value of the PCR associated with their design characteristics, such that the overall design and safety characteristics of the reactor are not sensitive to the value of the PCR. For other reactor design concepts a PCR which is both large and negative is an important aspect in the design of their engineered systems for controlling reactivity. It will be demonstrated that during Loss of Regulation Control (LORC) and Large Break Loss of Coolant Accident (LBLOCA) events, the impact of variations in power coefficient, including a hypothesized larger than estimated PCR, has no safety-significance for CANDU reactor design. Since the CANDU 6 PCR is small, variations in the range of values for PCR on the performance or safety of the reactor are not significant.

The method of the correlation and dispersion defining of the total power components in the electric transport devices

Purpose. Development and theoretical ground of the analytical method for the calculation of the active, reactive and total powers in the electric traction devices, taking into consideration the non-stationary character of the stochastic processes change of the voltage and current in the elements of these systems. Methodology. The mathematical methods of the random processes theory and the “discrete electrical engineering” methods are used for solving the main problem of this paper. Findings. The Method of the Correlation and Dispersion is developed for definition of the active power, the reactive power by Fryse and the total power of the devices in the elements of the electric traction system of the main-line railways. The method is based on the well-known concepts of auto- and inter-correlation functions of the random processes which govern the feeder voltages and the currents in the traction power supply subsystem as well as the currents and voltages of the electric rolling stock. The method developed in this paper allows estimating the powers of both stationary and non-stationary processes. This method can be used for the analysis of both the traction mode and the regenerative braking mode of the electric rolling stock. The total power components were calculated for the one of the feeder areas of the Prydniprovsk railway using this method. The results show the significant flow of the reactive power in the traction power supply system. This fact is also confirmed by the high values of the reactive power coefficient. Originality. Scientific novelty of the research is consisted in the following. Firstly, for defining the active and reactive powers in elements of the traction power supply system the new method (the Method of Correlation and Dispersion) is created and grounded. This method is different from other existing methods because it takes into consideration the varying non-stationary character of the chance processes of the feeder and substation voltages and currents. Secondly, in the DC traction power supply system the large values of the exchange reactive power by Fryze were created for the first time. Practical value.The method and its technique allow calculating the main energy coefficients for the traction power systems such are the reactive power coefficient, the main and additional active power losses in the power circuit of the electric rolling stockand the traction power supply system.

Prompt and power reactivity coefficients for the next generation VVER-1000 reactor including hexagonal assemblies and annular fuels

Many neutronics as well as thermal-hydraulics calculations have been made to find the performance of the proposed annular fuels (internally and externally cooled fuel pins) for both next generation PWRs and BWRs. Specifically, there has not been a significant study on the Russian type VVER-1000 reactors with annular fuels. Our aim herein is to study two important safety coefficients of the Iranian VVER-1000 core including hexagonal annular fuel assemblies at its BOC. The safety coefficients are “prompt reactivity coefficient” and “power reactivity coefficient”, where all simulations are made using MCNP-5 code. We found less (absolutely) Doppler coefficient for the next generation VVER-1000 and therefore Doppler coefficient decreasing is a good feature to avoid more resonance neutrons absorbing in the U-238; causes more fission density and also less soluble boron for core controlling (at the BOC) with comparing to the current VVER-1000 solid pins.

Thorium as an alternative fuel for SCWRs

This paper presents the research activity performed on a SCWR, which uses thorium fuel with 233U as fissile material. One- and two-dimensional calculations have been carried out to find the optimal assembly configuration including fuel pin diameters, pitches, number of fuel rings, etc. The goal has been to come up with an assembly configuration which has a conversion ratio higher than 1.0 for 233U, thus only the diminution of the 232Th has to be compensated. A two-pass configuration is proposed in order to combine the advantages of the regions with different coolant densities (without additional moderator). It is found that an assembly with pins of larger diameter in the high density coolant region and smaller ones in the low density coolant region is favorable since it minimizes the moderator-to-fuel volume ratio. Furthermore, an appropriate fitting of the regions is another measure to increase the conversion ratio. The two-dimensional calculations were followed by three-dimensional coupled neutronics – thermal hydraulics calculations, which prove that the assembly design is feasible from a neutronics point of view: the break-even point of FIR > 1.0 is achieved up to a burnup of 40.0 MWd/kgHM. Additionally, the fuel temperature and power reactivity coefficients have been determined. Both are negative proving the inherent safety of the reactor. A first sketch of the reactor pressure vessel including the flow path of the coolant is also presented.

Measurements of the isothermal, power and temperature reactivity coefficients of the IPR-R1 TRIGA reactor

The aim of this paper is to present the experimental results of the isothermal, power and temperature coefficients of reactivity of the IPR-R1 TRIGA reactor at the Nuclear Technology Development Center – CDTN in Brazil. The measured isothermal reactivity coefficient, in the temperature range measured, was −0.5 ¢/°C, and the reactivity measurements were performed at 10 W to eliminate nuclear heating. The reactor forced cooling system was turned off during the measurements. When the reactor is at zero power there is no sensible heat being released in the fuel, and the entire reactor core can be characterized by a single temperature. The power coefficient of reactivity obtained was approximately −0.63 ¢/kW, and the temperature reactivity coefficient of the reactor was −0.8 ¢/°C. It was noted that the rise in the coolant temperature has contributed only with a small fraction to the observed negative effect of the reactivity. The power defect, which is the change in reactivity taking place between zero power and full power (250 kW), was 1.6 $. Because of the prompt negative temperature coefficient, a significant amount of reactivity is needed to overcome temperature and allow the reactor to operate at the higher power levels in steady state.

Density effect of reactivity in a heavy-water power reactor operating in the 233U self-fueling regime

The void coefficients of the reactivity of different channel-type power reactors are compared. It is shown that a heavy-water channel reactor operating in a self-fueling regime within a uranium-thorium fuel cycle is just as nuclear-safe as CANDU type reactors. When composite fuel assemblies containing fuel elements with fuel and a ThO 2 target are used, such a reactor possesses negative void and therefore power coefficient of reactivity. Consequently, its nuclear safety is substantially higher than that of channel power reactors cooled by heavy or light water.

Uncertainty and sensitivity analysis of void and power reactivity coefficients in an RBMK-1500 reactor core

AbstractUncertainty and sensitivity analyses were performed for the calculation of power and void reactivity coefficients of an RBMK-1500 reactor core state. Both parameters are important for the reactivity feedback behaviour and are of special safety relevance. The reactivity coefficients were calculated using the 3D-reactor core model QUABOX/CUBBOX-HYCA and the uncertainty and sensitivity analyses were performed by the GRS methodology applying the SUSA software package (Software System for Uncertainty and Sensitivity Analysis). A total number of 20 uncertain input parameters and their probability distributions were identified as possibly relevant for the size of the reactivity effects and taken into account in the SUSA analysis. The method helps to identify the main contributors to the uncertainty of calculated results, as well as to determine two-sided (95 %, 95 %) statistical tolerance intervals of the investigated reactivity coefficients. The approach to quantify uncertain parameters for RBMK-1500 core calculations using the SUSA code package and QUABOX/CUBBOX-HYCA was successfully performed. The results provide guidance where model improvements should be performed to increase the accuracy of the calculations efficiently.

Modeling of void, fast power and graphite temperature reactivity coefficients measurements for the validation of RELAP5-3D RBMK-1500 reactor model

This paper deals with the modeling of RBMK-1500 specific transients taking place at Ignalina NPP: measurements of void and fast power reactivity coefficients, as well as change of graphite cooling conditions transient. The simulation of these transients was performed using RELAP5-3D code model of RBMK-1500 reactor. At the Ignalina NPP void and fast power reactivity coefficients are measured on a regular basis and based on the obtained experimental results the actual values of these reactivity coefficients are determined. Graphite temperature reactivity coefficient at the plant is determined by changing graphite cooling conditions in the reactor cavity. This type of transient is unique and important from the point of view of model validation for the gap between fuel channel and the graphite bricks. The measurement results, obtained during this transient, enabled to determine the thermal conductivity coefficient for this gap and to validate the graphite temperature reactivity feedback model. The performed validation of RELAP5-3D model of Ignalina NPP RBMK-1500 reactor allowed to improve the model, which in the future would be used for the safety substantiation calculations of RBMK-1500 reactors.

Reactor Dynamics and Stability Analysis of a Burst-Mode Gas Core Reactor, Brayton Cycle Space Power System

Reactor dynamics and system stability studies are performed on a conceptual burst-mode gaseous core reactor space nuclear power system. This concept operates on a closed Brayton cycle in the burst mode (on the order of 100-MW output for a few thousand seconds) using a disk magnetohydrodynamic generator for energy conversion. The fuel is a gaseous mixture of UF[sub 4] or UF[sub 6] and helium. Nonlinear dynamic analysis is performed using circulating-fuel, point-reactor-kinetics equations along with thermodynamic, lumped-parameter heat transfer and one-dimensional isentropic flow equations. The gaseous nature of the fuel plus the fact that the fuel is circulating lead to dynamic behavior that is quite different from that of conventional solid-core systems. For the transients examined, Doppler fuel temperature and moderator temperature feedbacks are insignificant when compared with reactivity feedback associated with fuel gas density variations. The gaseous fuel density power coefficient of reactivity is capable of rapidly stabilizing the system, within a few seconds, even when large positive reactivity insertions are imposed; however, because of the strength of this feedback, standard external reactivity insertions alone are inadequate to bring about significant power level changes during normal reactor operation. Additional methods of reactivity control, such as changes in the gaseousmore » of fuel mass flow rate or core inlet pressure, are required to achieve desired power level control. Finally, linear stability analysis gives results that are qualitatively in agreement with the nonlinear analysis.« less

Analysis of harmonic control systems of power distribution in a reactor

This paper investigates a comparatively new algorithm of harmonic (modal) control of power distribution. A digital reactor simulation program provided the methodological basis for the study. The approach to power distribution control systems based on the harmonic model of the controlled reactor enabled the authors to establish analytical criteria and to derive qualitative estimates of stability, efficiency, and noise-tolerance of various control structures. The authors demonstrate the proposed procedure for the case of a totalpower control system in a reactor with ''fast'' power coefficient of reactivity using a single control rod at the core center. Results of the study are presented in detail. The authors note that the implementation of a space-time filter in reactor control systems utilizing the harmonic control principle with the number of control rods and sensors exceeding the number of controlled harmonics opens certain new control possibilities and in some cases increases control effectiveness.

Simple Method to Predict Power Level and Core Flow Rate of Boiling Water Reactors by Using One-Point Core Model

A simple one-point core model has been developed to predict startup and load following features of boiling water reactors (BWRs). The variables used in this model are core thermal power, core flow rate, xenon concentration and control rod pattern, where the last variable is expressed in terms of the corresponding thermal power at the rated core flow. The number of parameters to be identified is only three, and they are determined by flow control line, xenon reactivity coefficient and power reactivity coefficient. These parameters can be adjusted by using the actual operating data of BWR plants. The accuracy of the one-point core model was evaluated in some typical startup operations of a reference 800 MWe class BWR. The prediction errors of the model were within 2% of relative power in comparison with results of a three-dimensional BWR core simulator and within 3% in comparison with the operating data. Use of this one-point core model, with xenon-iodine maps, should successfully predict reactor conditions, even when employing only simple hand-calculations.

Simple method to predict power level and core flow rate of boiling water reactors by using one-point core model.

A simple one-point core model has been developed to predict startup and load following features of boiling water reactors (BWRs). The variables used in this model are core thermal power, core flow rate, xenon concentration and control rod pattern, where the last variable is expressed in terms of the corresponding thermal power at the rated core flow. The number of parameters to be identified is only three, and they are determined by flow control line, xenon reactivity coefficient and power reactivity coefficient. These parameters can be adjusted by using the actual operating data of BWR plants. The accuracy of the one-point core model was evaluated in some typical startup operations of a reference 800 MWe class BWR. The prediction errors of the model were within 2% of relative power in comparison with results of a three-dimensional BWR core simulator and within 3% in comparison with the operating data. Use of this one-point core model, with xenon-iodine maps, should successfully predict reactor conditions...

Parameter identification for spatial xenon transient analysis and control

The real-time, on-line control of xenon-induced spatial flux oscillations in a large PWR requires the use of fairly simple models of the process for minicomputer implementation. Model simplification requires that the analyst reduce the physical phenomena to mathematical terms with coarser approximations and greater inaccuracies. In order to make a model's behavior fit that of a reactor as closely as possible, the estimation of parameters in the model requires special care. Three parameters were chosen for identification: the diffusion coefficient, D; the power reactivity coefficient, α F; and the microscopic 135Xe cross section, σ x . The method of maximum likelihood was used to obtain estimates of these parameters by comparing calculated results with actual plant data. Numerical values of these parameters are presented.

Coolant Flow and Reactivity Oscillations

The theoretical linear reactivity feedback model is analyzed and it is shown that the separate oscillations of reactivity, primary coolant flow, and secondary coolant flow provide valuable information such as the fuel power reactivity coefficient, the fuel temperature coefficient, and heat transfer characteristics between fuel and coolant.